Quantum Dot Version of Berry's Phase: Half-Integer Orbital Angular Momenta

TL;DR

This paper demonstrates that circular quantum dots with an odd number of electrons exhibit a Berry's phase of π, leading to half-integer orbital angular momentum values, supported by experimental evidence.

Contribution

It reveals a new realization of Berry's phase in quantum dots, linking topological phase to half-integer angular momentum due to symmetry and the Pauli principle.

Findings

Berry's phase for odd-electron quantum dots is π.

Eigenvalues of orbital angular momentum are half-integers.

Experimental results support the theoretical predictions.

Abstract

We show that Berry's geometrical (topological) phase for circular quantum dots with an odd number of electrons is equal to \pi and that eigenvalues of the orbital angular momentum run over half-integer values. The non-zero value of the Berry's phase is provided by axial symmetry and two-dimensionality of the system. Its particular value (\pi) is fixed by the Pauli exclusion principle. Our conclusions agree with the experimental results of T. Schmidt {\it at el}, \PR B {\bf 51}, 5570 (1995), which can be considered as the first experimental evidence for the existence of a new realization of Berry's phase and half-integer values of the orbital angular momentum in a system of an odd number of electrons in circular quantum dots.